Subgroups — #26236169

Order 12032.

784 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20244325	C₂	1	1	yes	maximal, characteristic
3	#20243946	C₂	1	2	yes	maximal
4	#20243944	C₂	1	2	yes	maximal
5	#20243539	C₂	1	1	yes	maximal, characteristic
6	#20243503	C₂	1	2	yes	maximal
7	#20243253	C₂	1	1	yes	maximal, characteristic
8	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
9	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
10	#20243236	C₂	1	2	yes	maximal
11	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₄	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₄	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
22	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
23	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
24	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
25	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
28	C₄²×Dic₄₇	C₂²	1	2	yes	—
29	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	#15688877	C₂²	1	1	yes	characteristic
33	#15688877	C₂²	1	1	yes	characteristic
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#336	C₂²	1	2	yes	—
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	Q₈×Dic₄₇	—	2	4	no	—
45	Q₈×Dic₄₇	C₈	1	8	yes	complemented
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	Dic₄₇⋊C₈	—	2	2	no	—
64	Dic₄₇⋊C₈	—	4	2	no	—
65	Dic₄₇⋊C₈	Q₈	1	4	yes	complemented
66	C₄×C₄₇⋊C₈	—	2	2	no	—
67	C₈×Dic₄₇	—	4	2	no	—
68	C₈×Dic₄₇	—	4	2	no	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₄₇	—	2	2	no	—
77	C₄×Q₈×C₄₇	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₄₇	—	2	2	no	—
83	C₄×C₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	#41	1	2	yes	—
112	C₄²×C₄₇	#41	1	2	yes	—
113	C₄⋊Dic₄₇	—	2	4	no	—
114	C₄⋊Dic₄₇	C₂×C₈	1	8	yes	—
115	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
116	C₄⋊Dic₄₇	M₁₆	1	4	yes	—
117	C₄×Dic₄₇	—	2	2	no	—
118	C₄×Dic₄₇	—	2	2	no	—
119	C₄×Dic₄₇	—	2	1	no	—
120	C₄×Dic₄₇	—	2	2	no	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	4	no	—
123	C₄×Dic₄₇	—	2	4	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	4	1	no	—
126	C₄×Dic₄₇	—	4	2	no	—
127	C₄×Dic₄₇	C₂×C₈	1	8	yes	—
128	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
129	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
130	C₄×Dic₄₇	#41	1	2	yes	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
140	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
141	Q₈×C₄₇	—	2	8	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	#117	1	2	yes	—
150	C₂×C₄×C₄₇	#117	1	2	yes	—
151	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
152	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	1	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	1	no	—
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
172	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
173	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
174	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
175	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
176	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
177	C₂×Dic₄₇	#131	1	2	yes	—
178	C₈×C₄₇	—	2	2	no	—
179	C₈×C₄₇	—	4	1	no	—
180	C₈×C₄₇	—	4	2	no	—
181	C₄₇⋊C₈	—	2	2	no	—
182	C₄₇⋊C₈	—	4	1	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	#22821	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
187	C₂²×C₄₇	#520	1	1	yes	characteristic
188	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
189	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
191	C₂²×C₄₇	#568	1	1	yes	characteristic
192	C₄×C₄₇	—	2	4	no	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	#431	1	4	yes	—
196	C₄×C₄₇	#554	1	1	yes	characteristic
197	C₄×C₄₇	#556	1	1	yes	characteristic
198	C₄×C₄₇	#557	1	1	yes	characteristic
199	C₄×C₄₇	#559	1	1	yes	characteristic
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	2	4	no	—
202	Dic₄₇	—	2	2	no	—
203	Dic₄₇	—	2	4	no	—
204	Dic₄₇	—	4	1	no	—
205	Dic₄₇	C₈×Q₈	1	4	yes	—
206	C₄²×Q₈	—	47	1	no	—
207	#1984	—	47	1	no	—
208	#1984	D₄₇	1	1	yes	characteristic
209	#1916	—	47	2	no	—
210	#1916	—	47	2	no	—
211	#1842	—	47	1	no	—
212	#1831	—	47	2	no	—
213	C₈×C₄⋊C₄	—	47	1	no	—
214	C₈×C₄⋊C₄	—	47	1	no	—
215	C₄×C₄⋊C₈	—	47	1	no	—
216	C₄×C₄⋊C₈	—	47	2	no	—
217	C₂×C₄₇	#2355	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
219	C₂×C₄₇	#2925	1	1	yes	characteristic
220	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
221	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
222	C₂×C₄₇	#2988	1	1	yes	characteristic
223	C₂×C₄₇	#2990	1	1	yes	characteristic
224	C₂×C₄×Q₈	—	47	1	no	—
225	C₂×C₄×Q₈	—	47	1	no	—
226	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
227	C₂×C₄⋊C₈	—	47	1	no	—
228	C₂×C₄⋊C₈	—	47	1	no	—
229	C₂×C₄⋊C₈	—	47	2	no	—
230	C₂×C₄⋊C₈	—	47	1	no	—
231	C₂×C₄⋊C₈	—	47	2	no	—
232	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	—	47	2	no	—
235	C₂×C₄×C₈	—	47	2	no	—
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₄×C₄⋊C₄	—	47	1	no	—
238	C₄×C₄⋊C₄	—	47	2	no	—
239	C₄×C₄⋊C₄	—	47	2	no	—
240	C₄×C₄⋊C₄	—	47	1	no	—
241	C₄×C₄⋊C₄	—	47	2	no	—
242	C₄×C₄⋊C₄	—	47	1	no	—
243	C₄³	—	47	2	no	—
244	C₄³	—	47	1	no	—
245	#336	—	47	2	no	—
246	#336	—	47	2	no	—
247	#336	—	47	1	no	—
248	#336	—	47	1	no	—
249	#336	—	47	2	no	—
250	#336	—	47	2	no	—
251	#336	C₂×D₄₇	1	2	yes	—
252	#336	C₂×D₄₇	1	2	yes	—
253	C₄₇	#22821	1	1	yes	characteristic, complemented, Sylow
254	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	47	2	no	—
258	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
260	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	—	47	8	no	—
264	C₄×Q₈	—	94	4	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₄⋊C₄	—	47	1	no	—
267	C₂×C₄⋊C₄	—	47	1	no	—
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
271	C₂×C₄²	—	47	2	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	—	47	2	no	—
275	C₂×C₄²	—	47	1	no	—
276	C₂×C₄²	—	47	2	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	47	2	no	—
279	C₂×C₄²	—	47	1	no	—
280	C₂×C₄²	—	47	2	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
283	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	47	4	no	—
286	C₄⋊C₈	—	94	2	no	—
287	C₄⋊C₈	—	94	4	no	—
288	C₄⋊C₈	—	94	2	no	—
289	C₄⋊C₈	—	188	2	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	94	2	no	—
292	C₄×C₈	—	188	2	no	—
293	C₄×C₈	—	188	2	no	—
294	#95	—	47	2	no	—
295	#95	—	47	2	no	—
296	#95	—	47	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₈×D₄₇	1	4	yes	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	2	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	2	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
307	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
309	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	1	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	Q₈×D₄₇	1	2	yes	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	47	8	no	—
332	C₄⋊C₄	—	47	4	no	—
333	C₄⋊C₄	—	47	4	no	—
334	C₄⋊C₄	—	94	4	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	47	8	no	—
338	C₄²	—	47	4	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	47	2	no	—
341	C₄²	—	94	2	no	—
342	C₄²	—	94	4	no	—
343	C₄²	—	94	4	no	—
344	C₄²	—	94	2	no	—
345	C₄²	—	94	2	no	—
346	C₄²	—	94	1	no	—
347	C₄²	—	94	2	no	—
348	C₄²	—	94	1	no	—
349	C₄²	—	188	1	no	—
350	C₄²	—	188	2	no	—
351	C₄²	#10625352	1	2	yes	—
352	C₄²	#10625352	1	2	yes	—
353	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
354	Q₈	—	2	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	47	2	no	—
363	C₂×C₄	—	47	2	no	—
364	C₂×C₄	—	47	2	no	—
365	C₂×C₄	—	47	2	no	—
366	C₂×C₄	—	47	4	no	—
367	C₂×C₄	—	47	2	no	—
368	C₂×C₄	—	47	4	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	1	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	1	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	1	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	94	1	no	—
378	C₂×C₄	—	94	1	no	—
379	C₂×C₄	—	94	1	no	—
380	C₂×C₄	#13093980	1	2	yes	—
381	C₂×C₄	#13093980	1	2	yes	—
382	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
383	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
384	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
385	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
386	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
388	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
389	C₂×C₄	#13094070	1	1	yes	characteristic
390	C₂×C₄	#13094072	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	94	2	no	—
395	C₈	—	188	1	no	—
396	C₈	—	188	2	no	—
397	C₂²	C₂×#13093980	1	1	yes	characteristic
398	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
399	C₂²	#15689605	1	1	yes	characteristic
400	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
401	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
402	C₂²	#131×D₄₇	1	1	yes	characteristic
403	C₂²	#15689888	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	47	4	no	—
408	C₄	—	94	4	no	—
409	C₄	—	94	2	no	—
410	C₄	—	94	4	no	—
411	C₄	—	94	2	no	—
412	C₄	—	188	1	no	—
413	C₄	#15689173	1	4	yes	—
414	C₄	#15689831	1	1	yes	characteristic
415	C₄	#15689844	1	1	yes	characteristic
416	C₄	#15689848	1	1	yes	characteristic
417	C₄	#15689855	1	1	yes	characteristic
418	C₂	#20246344	1	1	yes	characteristic
419	C₂	C₂×#15689173	1	1	yes	characteristic
420	C₂	#20252050	1	1	yes	characteristic
421	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
422	C₂	#20252340	1	1	yes	characteristic
423	C₂	#20252498	1	1	yes	characteristic
424	C₂	#20252512	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1984	C₂
socle, prime radical	C₂³×C₄₇	C₂³×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#22821
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1984

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
45. Q₈×Dic₄₇	C₈	semidirect
65. Dic₄₇⋊C₈	Q₈	semidirect
253. C₄₇	#22821	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×Q₈×Dic₄₇	2
#20244325	2
#20243946	2
#20243944	2
#20243539	2
#20243503	2
#20243253	2
C₈×C₄⋊Dic₄₇	2
C₄×Dic₄₇⋊C₈	2
#20243236	2
C₄₇×#1984	2
#22821	47